1728 (number)

List of numbers — Integers ← 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	One thousand, seven hundred [and] twenty-eight
Ordinal	1728th
Factorization	$2^6 \cdot 3^3$
Roman numeral	MDCCXXVIII
Binary	11011000000
Octal	3300
Duodecimal	1000
Hexadecimal	6C0

1728 is the natural number following 1727 and preceding 1729. 1728 is a dozen gross, one great gross (or grand gross, or, in Germanic, Mass).

In mathematics

It is the cube of 12 and, as such, is important in the duodecimal number system. It is the number of cubic inches in a cubic foot. 1728 occurs in the algebraic formula for the j-invariant of an elliptic curve. As a consequence, it is sometimes called a Zagier as a pun on the Gross–Zagier theorem.

• 1728 = 12³
• 1728 = 3³ × 4³
• 1728 = 2³ × 6³
• 1728 = 6³ + 8³ + 10³
• 1728 = 24² + 24² + 24²

17 = 2 + 3 + 5 + 7         (The sum of the first four prime numbers)

28 = 2 + 3 + 5 + 7 + 11 (The sum of the first five prime numbers)